I am still not seeing any evidence of your assertions. Dragon Age is a game with an abundance of background lore and the sources relevant to this topic suggest the opposite of your personal conclusions. You cannot simply make things up.
Well, according to the last thread I remember this argument coming up on, WoT describes the royal family of Rivain as "Chantry faithful, but progressive by necessity." You can argue that allowing some dissent is to their credit, but unless Drasanil paraphrased until the actual meaning was lost, that's not what's happening; it really sounds like the dissent would happen whether or not they were okay with it.
And apparently the royal family of Rivain are the closest thing Llomeryn has to rulers. Someone of whom that's true is either really libertarian, or just not entirely in control of their own country. Now, I can believe a slum not being entirely under the control of the rulers of the country, but Llomeryn is home to a bunch of pirates that are enough of a danger to extort protection money. If the Rivaini rulers were otherwise in control of their country, one would think they'd turn the entire population on that island.
Of course, none of that is entirely direct, and so if you gave me any "sources relevant to this topic" that "suggest the opposite of my personal conclusions" I might have to drop this.
We do know that their system has lasted far longer than the Circle system. We know that their Mages benefit their society as a whole. Clearly they are doing something right. As for Avvar and Spirits, if you bring Solas with you when you meet the Auger he says himself that it is safe. Spirits become Demons when their desires or purpose is corrupted in some way and according to Solas there is a degree of choice involved. The Spirits that align themselves with the Avvar are there because they want to be. The Avvar do not force them to do anything, it is a relationship of mutual communication.
Well, now that I've finally had the opportunity to look that up, I really have to say that that bit is less strong evidence for your arguments than I'd been letting Leaguer of One lead me to believe. Unless there's some dialogue that that player didn't get, all Solas is saying is that those spirits don't mean any harm. That's pretty obviously true, but not the evidence of the Avvar system as a whole being safe that I'll admit I'd been pretty sure I'd find in that video.
It does contain evidence that for your assertion that the friendly spirits try to protect the Avvar from demons, but they don't actually say much about how often they succeed. You'd imagine that it was most of the time, since the Avvar exist, but for all we know they could be losing clans at a fairly steady rate. Not a fast rate by most metrics, because otherwise there wouldn't be any Avvar, but a steady one is not impossible. Meanwhile it also contains evidence that there are demons to protect the Avvar from, and seems to lightly imply that not all of them started that way. That really seems to leave open the possibility of another Avvar god gone wrong, possibly even a game based on that problem.
If the Avvar caged their Mages it would have inevitably led to conflict and war like Circle.
That happened anyway. The Avvar weren't exactly united behind the Jaws of Hakkon. (Although given the power the Jaws alone had it's a good thing they weren't, since the Jaws were a threat to Orlais. If the Avvar had united they'd be a danger to all of humanity, and the other races besides.)
No system is foolproof. That is an impossible standard.
Does that mean the Circle having a civil war every few centuries, and an Annulment an average of twice a century, isn't all that bad?
Clearly the Mages disagreed.
Clearly some of the mages disagreed. That "the mages" disagreed is less clear. I don't think we're ever actually shown to what extent the mages as a whole wanted the result they got.
My understanding is that the vote in Asunder that really kicked things off happened after things went all to hell thanks to a combination of Lambert's inept PR and Adrian's amoral and cynical manipulation. I can see a mage who wants the Circle deciding that they aren't getting what they want and just acknowledging that the system is gone, and voting accordingly.
For that matter I don't think it's made clear that the deciding vote (the Aequitarian representative) knew what the Aequitarian fraternity wanted; he only just became their representative, and would have to have gotten an accurate read of them over the course of his time in the fraternity, not to mention that nobody's ever told me he even tried. Admittedly I haven't actually read the book and am just basing all of this off the way other pro-templars characterize things, but I don't remember ever seeing a pro-mage answer any of this.
Here's where we get into the stuff I personally can swear to: even after the vote, the Hasmal and Montsimmard Circles still had mages loyal to the system inside them, despite some of the Libertarians in Monstimmard killing mages who were loyal to the Circle. (Who struck first is not made clear; Vivienne is lightly implied to believe the rebels were at fault, but she doesn't back it up. Anyway, that is not central to my point; my point is that there were loyalists.)
And while I haven't played Trespasser, my understanding is that no matter which Divine you pick, there is a Circle of Magi despite the fact that the mages can't really be forced to be part of it anymore in Leiliana's ending. So some clearly still wanted to be a part of it.
I fail to see how a cage, however gilded, is beneficial to anyone other than those who hold the key.
I tried to remedy that, but let's try it again.
It keeps people out as easily as it keeps them in. There are lynch mobs after mages, and while the Chantry's teachings and the existence of Tevinter might be responsible for some of that, I don't remember anyone ever giving a good answer to the point that it's partially because mages are legitimately scary. When Wynne and her group are confronted by a bunch of ornery peasants who seem to have been going in that direction, the peasants clearly don't care about the Chantry's unproven accusations about the Black City. One thing they mention is the assassination attempt on the Divine, (which you can argue was the Chantry's fault, though I personally disagree) but the fact remains that they've found reason enough to be scared of mages around their own community. (Some of it is questionably magical, but enough of it isn't that better education would mitigate the problem rather than solving it. Not that that wouldn't be on my to-do list if I ruled Thedas.)
Besides which, the gilded cage also comes with some fringe benefits that the mages would have had difficulty getting otherwise. Meals, board, and an education. The education isn't even just magical training: the mages seem to be literate in a setting where you really can't assume your average man on the street is. You can argue that the mages should be free to seek that out on their own, but this doesn't seem to be a setting where they have any guarantee of success, and a mage who fails to gain meals is a pretty serious danger.
And not to put too fine a point on it, but mundanes benefiting at mages expense is not the worst that can happen. Mundanes are the majority faction. If a system legitimately makes mundanes safer at mages expense, it's not as bad as mages being freer at the expense of mundanes.